A164784 -id:A164784 - cp's OEIS frontend

A193871 Square array T(n,k) = k^n - k + 1 read by antidiagonals.

1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 25, 13, 1, 1, 31, 79, 61, 21, 1, 1, 63, 241, 253, 121, 31, 1, 1, 127, 727, 1021, 621, 211, 43, 1, 1, 255, 2185, 4093, 3121, 1291, 337, 57, 1, 1, 511, 6559, 16381, 15621, 7771, 2395, 505, 73, 1, 1, 1023, 19681, 65533, 78121, 46651, 16801, 4089, 721, 91, 1

Offset: 1

Omar E. Pol, Aug 21 2011

The columns give 1^n-0, 2^n-1, 3^n-2, 4^n-3, 5^n-4, etc.

The main diagonal gives A006091, which is a sequence related to the famous "coconuts" problem.

			Array begins:
  1,   1,    1,     1,     1,    1,    1,   1,   1,   1
  1,   3,    7,    13,    21,   31,   43,  57,  73
  1,   7,   25,    61,   121,  211,  337, 505
  1,  15,   79,   253,   621, 1291, 2395
  1,  31,  241,  1021,  3121, 7771
  1,  63,  727,  4093, 15621
  1, 127, 2185, 16381
  1, 255, 6559
  1, 511
  1

M. B. Richardson, A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Coconuts Problem, The Winnower, 3 (2016), e147175.52128. doi: 10.15200/winn.147175.52128

Row 1: A000012. Rows 2,3: A002061, A061600 but both without repetitions.
Columns 1..10: A000012, positives A000225, A058481, A141725, A164785, A164784, A164783, A164786, A177095, A170955.
Cf. A276135.

Table[k^# - k + 1 &[n - k + 1], {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Nov 16 2016 *)

A253209 a(n) = 6^n + 5.

Original entry on oeis.org

6, 11, 41, 221, 1301, 7781, 46661, 279941, 1679621, 10077701, 60466181, 362797061, 2176782341, 13060694021, 78364164101, 470184984581, 2821109907461, 16926659444741, 101559956668421, 609359740010501, 3656158440062981, 21936950640377861, 131621703842267141

Offset: 0

Vincenzo Librandi, Dec 29 2014

Subsequence of A226814.

Index entries for linear recurrences with constant coefficients, signature (7,-6).

Cf. similar sequences listed in A253208.

Cf. A164784, A226814.

Magma
```
[6^n+5: n in [0..30]];
```
Mathematica
```
Table[6^n + 5, {n, 0, 30}]
```

G.f.: (6 - 31*x) / ((1 - x)*(1 - 6*x)).

a(n) = 7*a(n-1) - 6*a(n-2) for n>1.

cp's OEIS Frontend

A193871 Square array T(n,k) = k^n - k + 1 read by antidiagonals.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica